It is for this reason that they believed the
motions of the heavenly bodies to be based on circles and spheres. Nothing less than
perfection could account for the behaviour of objects so close to the Gods. The problem
was that when they looked carefully at the motion of the planets, they observed some
pretty irregular motion. Some planetes would actually retrace their steps in the sky
at certain times, instead of moving along a smooth continuous arc. In order to retain
the symmetry principle, Ptolemy figured out that by adding circles within circles
(called ``epicycles'') it was possible to account for such ``retrograde'' motion, as it
was called. However, as observations got better and better, it was necessary to
add more and more circles within circles, until the perfection of the underlying
geometrical shape (the circle) was completely overshadowed by the complexity of
the model. Moreover, by adding enough circles, it is possible to reproduce any orbit
whatsoever, so this model lacks the essential feature of being falsifiable, and does
not qualify as a scientific theory. It therefore appears that this was a misguided
application of symmetry. As it turns out the symmetry principle was not so bad. It
was the geocentric viewpoint (i.e. the notion that the Earth was the center of the
Universe) that messed them up. Once it was realized, by Copernicus, that the Sun
was the center of planetary motion and not the Earth, then the orbits of the planets
once again became very nearly circular.